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10. Simplify the following expression:

[tex]\[5.04 \times 10^{-2} + 12 \times 10^{-3} - 2.04 \times 10^{-2} - 8.52 \times 10^{-3}\][/tex]



Answer :

GinnyAnswer
Certainly! Let's solve the expression step-by-step:

10. \(5.04 \times 10^{-2} + 12 \times 10^{-3} - 2.04 \times 10^{-2} - 852 \times 10^{-4}\)

### Step 1: Convert each term from scientific notation to decimal form

1. \(5.04 \times 10^{-2}\)
[tex]\[ 5.04 \times 10^{-2} = 0.0504 \][/tex]

2. \(12 \times 10^{-3}\)
[tex]\[ 12 \times 10^{-3} = 0.012 \][/tex]

3. \(2.04 \times 10^{-2}\)
[tex]\[ 2.04 \times 10^{-2} = 0.0204 \][/tex]

4. \(852 \times 10^{-4}\)
[tex]\[ 852 \times 10^{-4} = 0.0852 \][/tex]

### Step 2: Substitute the converted values back into the expression

[tex]\[ 0.0504 + 0.012 - 0.0204 - 0.0852 \][/tex]

### Step 3: Perform the addition and subtraction in sequence

1. Add \(0.0504\) and \(0.012\):
[tex]\[ 0.0504 + 0.012 = 0.0624 \][/tex]

2. Subtract \(0.0204\) from \(0.0624\):
[tex]\[ 0.0624 - 0.0204 = 0.042 \][/tex]

3. Finally, subtract \(0.0852\) from \(0.042\):
[tex]\[ 0.042 - 0.0852 = -0.0432 \][/tex]

### Final Answer:
[tex]\[ 5.04 \times 10^{-2} + 12 \times 10^{-3} - 2.04 \times 10^{-2} - 852 \times 10^{-4} = -0.0432 \][/tex]

So, the computed value of the given expression is [tex]\(-0.0432\)[/tex].

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